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zbw Leibniz-Informationszentrum WirtschaftLeibniz Information Centre for Economics
Roosen, Jutta; Hennessy, David A.
Working Paper
Seasonality, capital inflexibility, and theindustrialization of animal production
FE working paper // University of Kiel, Department of Food Economics and ConsumptionStudies, No. 0401
Provided in Cooperation with:Christian-Albrechts-University of Kiel, Department of Food Economicsand Consumption Studies
Suggested Citation: Roosen, Jutta; Hennessy, David A. (2004) : Seasonality, capital inflexibility,and the industrialization of animal production, FE working paper // University of Kiel, Departmentof Food Economics and Consumption Studies, No. 0401
This Version is available at:http://hdl.handle.net/10419/38623
Seasonality, Capital Inflexibility, and the Industrialization of Animal Production
2
Seasonality, Capital Inflexibility, and the Industrialization of
Animal Production
by
Jutta Roosen and David A. Hennessy*
January 2004
Authors are professor at the Department of Food Economics and Consumption Studies, University of Kiel, Germany, and at the Department of Economics, Iowa State University, USA, respectively. They would like to thank Oya Erdogdu, John Miranowski, HongLi Feng, and Don Blayney for comments and useful guidance.
Roosen is the corresponding author. She can be reached at Department of Food Economics and Consumption Studies, University of Kiel, Olshausenstr. 40, 24098 Kiel, Germany. Ph.: +49 431 880 4567, Fax: +49 431 880 7308, e-mail: jroosen@food-econ.uni-kiel.de.
Seasonality, Capital Inflexibility, and the Industrialization of Animal
Production
Abstract
Among prominent recognized features of the industrialization of animal production over the past
half century are growth in the stock of inflexible, or use-dedicated capital, as an input in
production, and growth in productivity. Less recognized is a trend toward aseasonal production.
We record the deseasonalization of animal production in the US and European countries over the
past 70 years. We also suggest that A) lower seasonality can precede or Granger-cause increased
productivity due to increased capital intensity, and B) productivity improvements can Granger-
cause lower seasonality. Process A) should be more likely earlier in the industrialization
process. For US dairy production, our empirical tests find some evidence that process A)
operated early in the 20th Century while process B) operated in more recent times.
Keywords: Capital Intensity, Causality, Dairy, Regional Production Systems
1
Seasonality, Capital Inflexibility, and the Industrialization of Animal Production
Agriculture has become more capital intensive in most of the world during the latter part of the
20th Century. This capital deepening has occurred largely in the machinery, irrigation, and
buildings categories (Larson, Butzer, Mundlak, and Crego). The structural effects have been
particularly notable in animal agriculture in the developed world, where the phrases ‘factory
farming’ and ‘industrialized agriculture’ correctly depict an animal production process for hogs,
chickens, turkeys, and laying eggs that is broadly similar to the prototypical manufacture of
widgets. These large farms have increasingly automated production processes, and most workers
are employees with routinized tasks.
Field crop agriculture on the other hand, though greatly affected by mechanization and other
technological innovations, does not yet resemble an industrialized process. Allen and Lueck
argue convincingly that randomness due to weather is primarily responsible because it confounds
monitoring in the principal-agent relation, and it requires managerial focus when organizing
many mundane production activities. Strengthening control over animal agriculture has involved
largely strengthening the control of nature in the production process. Animals have been
confined, while seasonal aspects of biological behavior have been suppressed through breeding
or physiological interventions. Consequences have been the homogenization of the production
process and the growing affordability of cheap animal protein in much of the world.
Notwithstanding attention from several academic fields, the process of industrialization at
the sector level is not well-understood. This is so in agriculture and in other sectors. Most
economic studies on industrialization assume agriculture to be the reference non-industrial
sector, and their insights concerning the details of agriculture are limited. Technology in
agriculture is seen to matter because it frees up resources for other uses (Jorgenson; Scitovsky).
Kuznets does emphasize co-dependency, through spillover effects, between technical change in
agriculture and other sectors. This view sees agriculture developing along with other sectors so
that all sectors are comparably industrial. A facet of this viewpoint arises in the induced
2
innovation argument of Hayami and Ruttan. If the price of agricultural labor rises due to
increased demand from other sectors, then labor-saving innovations should be induced in
response over time.
Studies in economic history have shown evidence that interactions between agricultural
seasonality, non-agricultural industrialization, and productivity outside agriculture are likely
adverse because industrial plants are most efficient when labor supply is constant (Sokoloff and
Dollar; Sokoloff and Tchakerian; Anderson). Our interest is not in the role of agricultural
seasonality on external industries, but in its role on agriculture itself.
As to what industrialization is, it has many features involving firm behavior, industry
structure, the creation of new subsectors and change in the nature of sector products. We refer
the reader to Meeker, to Boehlje, or to Drabenstott on characterizations, and qualify the
components that we are interested in as primarily firm-level and industry-level behavior
regarding technologies used. The technologies should emphasize the control, systemization, and
routinization of processes in order to be more assured of product volume and quality at low cost
given the larger capital investment necessary for an industrial approach. Regarding the
efficiency effects of capital deepening, Chandler (p. 24) has written
“These potential cost advantages could not be fully realized unless a constant flow of materials through the plant or factory was maintained to assure effective capital utilization. If the realized volume of flow fell below capacity, then actual costs per unit rose rapidly. They did so because fixed costs remained much higher and “sunk costs” (the original capital investment) were also much higher than in the more labor-intensive industries.”
How industrialization arises is largely a question of structural dynamics because the process
is not instantaneous and there is no guarantee it will continue to the point where a sector or
economy is recognized as being industrialized. Some inquiries into the path taken suggest the
possibility of multiple equilibria (Murphy, Shleifer, and Vishny; Matsuyama; Gans, 1997; Chen
and Shimomura; Ciccone) so that the economy needs a ‘big push’ to industrialize. As Gans
(1998) has pointed out, the existence of multiple equilibria relies on the assumption that firms
3
face two technology choices where one is increasing returns and the other is a constant returns
reference technology. This ‘big push’ literature leads naturally to policy proposals on
engineering an equilibrium, typically a more industrial equilibrium given the increasing returns
to scale that are present. Due to its macro-economy nature, this area of work has little to say
about how the particulars of any given industry affect the industrialization process. Our interest
is focused on animal agriculture, and we intend to show that sector detail can provide insights on
the process.
The formal literature on explaining the agricultural industrialization process is quite sparse.
In one sense this is not surprising because the set of events presents somewhat of a conundrum.
Agricultural produce is largely commodity in character, while market size is both large and
stable. Management of on-farm processes does not require intensive formal training. These
technology attributes make the production of food quite like cloth or pin manufacture, and so an
explanation on the critical distinctions are warranted.
One theory is that agricultural industrialization is demand-led, through increasing demand by
consumers and food retailers for product and process information (Barkema; Drabenstott;
Kinsey). While likely a facet of the subject, for industrialized agriculture can deliver higher
quality and more information, demand-side ideas have thus far explained little about the process.
The demand-side story is best at explaining changes in control and increasing vertical
coordination across much of the food sector. Consumers (or, more likely, their agents) want to
peer inside the farm in order to verify quality and caretaking behavior (Hennessy). Processors
seek knowledge on product attributes in order to better satisfy consumers. Demand-side
arguments do not explain why crop agriculture is not industrial. Nor does it explain common
features in the technologies that tend to accompany industrialization. Part of the answer must lie
in the nature of the process and product.
Allen and Lueck, in extending insights by Becker and Murphy on the importance of
information in coordinating activities, hold that noise and other irregularities in the production
4
process are a reason that crop agriculture has not industrialized. Hennessy, Miranowski, and
Babcock go further to suggest that biotechnology innovations can promote three features of
industrialization. These are demand for tight control over the production environment, strong
productivity growth, and an increasingly differentiated product. Motivated by Chandler, in this
paper we consider two other features of agricultural industrialization; the roles of low variability
in throughput and enterprise-dedicated capital in enhancing productivity.1
Briefly our problem is as follows. Animal production has tended to be seasonal due largely
to the biology of the animals themselves and the plants they are fed on. Seasonal production had
faced the problem of perishability, together with the unpleasant consequences of storage
technologies (e.g., salting). Refrigeration, ease of transportation, and growing international trade
have largely solved these problems, though at a modest cost (Goodwin, Grennes, and Craig).
These, by themselves, should promote the extent of production seasonality and yet we will show
that animal production seasonality has declined in recent decades. The resolution of the
conundrum lies, we believe, partly in the inflexible nature of capital investments. Unlike labor
and the versatile tractor, most other investments in animal agriculture tend to be inflexible in
adapting efficiently to seasonality because machines are often dedicated to a particular use.
The intent of this paper is threefold. We will complement earlier work by Erdogdu on the
United States by recording the deseasonalization of animal production using time series and
statistical trends available for pork, beef, and (mostly) milk production in the Northern
Hemisphere during the latter part of the 20th century. We will propose a theory on the origins of
this deseasonalization, and on what it means for the industrialization of agriculture. We will also
test this theory.
Our analysis is structured as follows. After this introduction, we focus on dairying to review
some of the most important trends in animal production in the developed world during the last 50
1 Jovanovic and Rousseau provide evidence in favor of growth in enterprise-dedicated capital used by US corporations to motivate a theory on trends in the division of surplus.
5
years. Based on monthly production data for dairy, beef and pork in various countries, we
present and discuss seasonality indicators. We then develop a brief causal model of diminishing
seasonality. Hypotheses emerge concerning causal relationships between capital intensity and
seasonality indices, and we test for evidence on these hypotheses.
The Seasonal Dimension: Dairying
While we see no reason that our theory would not apply to other animal products, we focus
attention on dairying for two reasons. First, data on monthly production is readily available and
interpretable across several countries. Second, the issue is topical in the dairy sector because
traditional systems of more seasonal production remain viable whereas poultry meats, eggs, and
hogs are now produced overwhelmingly in non-seasonal systems.
In the traditional United States dairy areas of the Upper Midwest, New England and New
York, cows were grazed outdoors during the warmer half of the year. This approach took
advantage of cheap in-situ grass while surplus grass and other crops made for cheap fodder
during the winter when cows were confined. Cows tended to be calved in Spring to match
lactation with grass growth. In part because of the perishability of liquid milk and in part
because of milk marketing regulations, other regions also produced milk. Dairy farms in some
of these regions, especially California, tended to be very different. Scale of production tended to
be larger, output was less seasonal and cows were largely confined, i.e., in dry-lot. During the
period 1950-2000, production in the West has expanded at the expense of the traditional regions
and the expanding farms have tended to be more industrial in format.2
Table 1 provides an overview of some of the main innovations in United States on-farm
dairy production over the last Century. We categorize them as pro-seasonal, neutral, or anti-
seasonal. The pro-seasonal innovations are provided in the first column. Electric fencing has
greatly improved efficiency of in-situ grazing, while irrigation technologies have assisted in
6
reducing the weather risk of an outdoor production system. Forage preservation techniques have
improved grass utilization efficiency and have helped to maintain the contribution of grass
products to the dairy cow diet. These innovations have acted to alter seasonal costs. Final
product storage innovations, P4, on the other hand, separate the timing of production from
consumption and so allow for more intensive production in low-cost seasons.
Concerning entries in the seasonality neutral column, genetic innovations have increased
dramatically the milking cow’s productivity. The consequences for seasonality are not readily
apparent beyond making two points. The cow’s dry period at end of lactation has declined and
this is a very direct way in which increased productivity can cause deseasonalization. There is
also reason to believe that high yielding cows are less robust to weather and disease. They are
increasingly bred with a constitution that favors an indoor life, but that may be a consequence of
deseasonalization and not a cause. Antibiotics, N2, are a substitute for sanitation, N3. While the
confined cow is easier to monitor and maintain a health regime for, cleanliness can be a problem
and communicable disease can also be transmitted more quickly. Fertilization technologies have
reduced the costs of concentrate feed, forage, and in-situ grazing. In the absence of further
information, we place it in the seasonality neutral column. Finally, the tractor has proved to be
just as versatile around the farmyard as in the field and so the effect on the decision to confine
cows is not immediate.
The third column lists what we contend are anti-seasonal innovations. Artificial
insemination and housing innovations have diminished the roles of nature in animal production
and must be important components of sector industrialization. Entries A3 through A9 are of
particular interest to this paper, and involve the growing capitalization of animal agriculture. In
all cases the equipment put in place is dedicated and is inelastic with respect to inter-season
2 Blayney provides detailed perspectives on US production patterns in recent times.
7
substitution.3 As we will show, this inflexibility should be important in determining the rate of
deseasonalization. On A10, manure is spread as fertilizer but it is an inconvenient form of plant
nutrition. While all dairy production systems produce manure due to animal confinement, the
problem is most severe for a completely confined production system and so innovations in that
area have been most beneficial for non-seasonal production.
United States farms have become increasingly specialized in the outputs they produce, see
Gardner (p. 61). This likely means there are fewer other on-farm uses of dairy farm labor during
the low output season. Transportation innovations are also likely to have been anti-seasonal, if
only because feed and forage input markets have become more integrated and so less subject to
regional effects.
The direct importance of these developments for agricultural productivity has been studied
elsewhere in the literature. Of interest to us are their effects on seasonal structure in animal
production. In the next section we will provide statistical evidence on the nature of change in
animal production seasonality over time.
Documenting Seasonal Patterns in Agriculture
Table 2 reports the monthly production data series we have used from US, Canada (CAN), UK,
and German (DE) sources. The series have been transformed to take account of the different
length of the months in a year. That is, monthly production has been divided by the actual
number of days to yield average daily production and then normalized to a thirty-day month.
Seasonality of production has been measured by two concentration indices. Following
Erdogdu, who investigated animal production seasonality at US state level for hogs, milk and
3 For readers not familiar with modern capital intensive dairy farming and processing we reference Tamime and Law, where the extent and variety of commercial dairy mechanization and automation applications is documented. For on-farm US agriculture in general, real net (of depreciation) on-farm investment was positive for most years between 1945 and 1980. A decline in real capital investment occurred only with the farm crises of the 1980s (for data see p. 263 in Gardner, 2002).
8
beef, we use the Herfindahl index ( H ) and the maximum entropy index ( E ). Denoting month m
share, 1m for January and 12m for December, in annual production in year t as ,m ts ,
12
,11m tm
s , the year t value of H is calculated as 212
,1( 100)t m tmsH . Year t entropy is
12
, ,1ln( )t m t m tm
s sE . Because 2,( )m ts is convex whereas , ,ln( )m t m ts s is concave, an increase
in dispersion among monthly shares should be identified by a lower H and higher E . In fact,
for monthly production shares, E reaches a maximum of ln(12) = 2.4849 when an equal share of
1/12 is produced in each month whereas H has value 833.33 in this case.
For ease of interpretation we also report the peak-trough ratio of monthly production. In a
given year it is calculated as the ratio of production in the month where production is maximum,
tsmax, , to production in the month where production is minimum, tsmin, . The peak-trough ratio is
max, min,t t ts sR . By definition, R
values are limited to no less than unity and a value of one
would indicate constant production across months in a year. Note also that the peak and trough
months may differ across states and years. All analyses to follow have been performed on both
H and E
indices but results are very similar and we conserve space by only reporting results
using E . Descriptive statistics in the following tables are provided for R
and E as the former
lends itself most readily to intuitive interpretation.
Table 3a reports the calculated indices at the national level. It is obvious that seasonality has
declined over time. The most marked decline is in dairy production. Canada, in particular,
changed from a strongly seasonal to an essentially non-seasonal system over the period 1950-
2000. A similar trend, but to a lesser extent, is observable for pork. For beef, no clear trend
toward more or less seasonality is discernable. Table 3b reports the seasonal indices for 14
major US milk producing states, where monthly data were available from 1950 onwards.4 The
decline over time in seasonal dispersion is quite uniform across states.
4 States were selected on the availability of continuous monthly production data over 1950-2002.
9
An understanding of the table’s regional dimension requires some background on the
significance of states in the US dairy industry. Table 4 shows that Wisconsin and California
were the two most important milk production states in 2002. These states have had very
different production systems, Wisconsin having smaller herds and more pronounced production
seasonality.5 Since 1950, California had quadrupled production share to move from fourth to
first in production. Wisconsin’s production share grew from 12.7% to beyond 17% in 1980
before declining back toward 13%. The less significant Midwestern states have lost production
uniformly since 1950, Minnesota and Wisconsin being the exceptions and Minnesota’s relative
decline commenced circa 1970. The significant Eastern states of New York and Pennsylvania
saw a growth in national share before a relative decline set in over the twenty years commencing
about 1980. Southern states, small producers to begin with, have largely contracted while the
parched Western and Mountain states have expanded.
To understand the dynamics behind the decline in seasonality as reported in tables 3a and 3b,
we test the hypothesis that E is converging to a non-seasonal system. If deseasonalization
follows a geometric convergence process, then it can be modeled as 1 1( )t taE E E E ,
ln(12)E . This is equivalent to an autoregressive order 1 (AR1) process:
(1) 0 1 1,t ta aE E
with the restriction on the constant that 0 1(1 )a a E . In this process, a1 is the convergence
rate: the higher its value, the faster E converges to E .
The results are given in tables 5 and 6. These tables also provide test statistics for the
hypothesis H0: 0 1(1 )a a E , i.e., whether constant geometric convergence to the non-seasonal
system is an appropriate model. Looking at the results for the different countries in table 5, the
The chosen states represented 63% of US production in 1950 and 75% of production in 2000. 5 An interesting comparison of structural divergence between California and Wisconsin systems over 1950-1982 is provided in Gilbert and Akor, who show that the systems have diverged markedly in farm structure and input usage patterns.
10
hypothesis of geometric convergence is rejected in all cases except for milk in Canada and the
US. The convergence rates for milk vary between 0.842 in the UK and 0.975 in Canada.
Convergence rates are considerably lower, but still significant, for pork where they vary between
0.176 in Germany and 0.672 in the US. They are insignificantly different from zero for beef in
Germany and in the US. Table 6 reports similar results for the 14 US dairy states. Convergence
to a completely aseasonal system is rejected at the 5% significance level except for Minnesota.
Nonetheless significant convergence rates are observed, varying between 0.775 and 0.929.
Overall convergence rates in these states are lower than for the US as a whole. For both tables,
the estimated convergence parameters are sufficiently large to suggest the existence of a unit root
and we will formally test for unit roots at a later juncture.
As will be explained shortly, changes in animal productivity are important in our inquiry into
the nature of deseasonalization. Here we only have reliable indicators for milk in the US,
Canada, Germany and the UK, and for pork in the US. Milk yield per cow in liters or gallons is
used as the productivity indicator in dairying. Measures of hog productivity in the growing
phase are more difficult to obtain and we use the breeding phase indicator of farrowing sow
average litter size.
Theoretical Motivation
Our intention is to explore interactions between productivity and seasonality. Equipped with
these indicators and considering the dynamics of the seasonal structure of the dairy industry in
the US, table 7 shows correlations between seasonality, productivity, and production shares for
the 14 US dairy states listed in table 6. These correlations were calculated based on 1950 data
for the fourteen states, and again on 2000 data. In 1950, when the high seasonality systems of
the upper Midwest had the large shares in US total production, a negative correlation existed
between production shares (Shares) and aseasonality. This negative relationship turned into a
positive one in 2000 because by then the aseasonal western state production systems had large
11
shares in US production.
The relation between productivity and production shares is, as expected, positive in both
periods but it declined slightly from 0.459 in 1950 to 0.402 in 2000. This decline indicates that
other factors are important. We look next at motivating the closeness in relation between
aseasonality and productivity in the lower right part of the table. The relationship has always
been positive for the data periods covered but has become much stronger over the last 50 years,
increasing from 0.194 in 1950 to 0.358 in 2000.
Model
A representative farm produces animal output in two seasons; season A is high-cost while B is
low-cost. Outputs Aq and Bq are produced in seasons A and B, respectively. There are four
types of costs. There are seasonal unit costs labeled as Ac and Bc , respectively, where A Bc c
and these costs amount to A A B Bc q c q per annum. There is a season-dependent convex cost
function ( , )A BC q q that capture decreasing returns to scale. This cost function is also symmetric,
ˆ ˆ ˆ ˆ( , ) ( , )A A B B A B B AC q q q q C q q q q . There are season invariant unit costs labeled as c ,
and this unit cost parameter will change as a result of technical innovations. These costs amount
to A Bcq cq per annum. Finally, there are per annum peak-load unit capital costs amounting to
max[ , ]A BF q q . As with c , parameter F
can change as a result of technical innovations.
The price-taking firm obtains season invariant market price P per unit sold where the
assumption has been made that product is storable at zero cost. Firm annual profit is then
(2) ( ) ( ) ( , ) max[ , ].A B A A B B A B A BP c q q c q c q C q q F q q
Denote the optimal output choices as *Aq and *
Bq . The symmetry of ( , )A BC q q allows us to
readily conclude that optimum outputs satisfy * *( )( ) 0A B A Bc c q q , and so that * *A Bq q . We
characterize capital intensive innovations as follows. They increase unit peak load capital cost
F while also decreasing unit season-invariant cost c . The sorts of innovations considered here
12
include items A2 through A9 in table 1. The innovation will be adopted if the trade-off between
costs is sufficiently favorable. Using the envelope theorem on (2), profit increasing innovations
are ones that satisfy * * */ /( )B A Bc F q q q .
Characterize the distribution of trade-offs on available innovations /x c F as discrete
measure ( ) : ( ,0] [0,1]X where X is a set of form xx],,( ,
the non-
negative reals. The normalization to [0,1] is a convenience, and the most profitable among
available innovations to adopt are those with low x values. They reduce costs A Bcq cq
by
most relative to the cost increase arising from the required increase in F . Firms adopt
innovations with trade-offs up to the critical trade-off ratio * * */( )B A Bq q q so that set of adopted
capital intensive innovations among those available has measure * * *(( , /( )])B A Bq q q . This
measure is largest, at (( ,0.5]) , when the seasonality peak-trough ratio * */B Aq q is smallest.
PROPOSITION 1. As seasonality decreases, i.e., the peak-trough ratio decreases, then the rate
of adoption of capital intensive innovations increases.
The proposition can be interpreted in two ways. Suppose some multi-use innovation with a
barnyard application (e.g., electricity or vacuum tubes) is commercialized. If it so happens that
the innovation has an anti-seasonal bias, so that seasonality decreases, then one should see a
pick-up in the adoption of capital intense innovations that are already available to dairy
producers. Alternatively, viewing table 3b, one can take a regional perspective to conclude the
Wisconsin and Minnesota seasonal production systems should be less capital intensive than the
California system.
This proposition would, by itself, suggest that deseasonalization should precede productivity
growth when productivity growth is primarily in the form of season-inflexible capital. However,
the peak-load capital cost has another effect. Suppose that ( , )A BC q q takes the homothetic
constant elasticity of substitution form 1/ˆ( , ) [( ) ], 1A B A BC q q C q q . The optimality
13
condition for an interior solution with * *B Aq q is
(3) 1/( 1)*
*,B B
A A
q P c c F
q P c c
and, given A Bc c , consistency requires that A Bc c F . If instead A Bc c F then the farm
would not produce more in season B than in season A because the marginal cost of season B
production would (weakly) exceed that of season A production. Nor would the farm produce
more in season A because B Ac c F . So * *A Bq q when A Bc c F .
Differentiate (3) with respect to F , taking into account the associated change in c , /dc dF
0 , to obtain
(4) (2 ) /( 1)* *
2
( / ) 1 ( ) /| .
1 ( )B A B A A B
cchanges A A
d q q P c c F c c P c c F dc dF
dF P c c P c c
The number is negative when A Bc c F , and so more capital intensity decreases the peak-
trough ratio. When A Bc c F , then * *A Bq q remains valid under the higher F value.
PROPOSITION 2. Let 1/ˆ( , ) [( ) ], 1A B A BC q q C q q , with A Bc c . Let capital intensity
increase, i.e., F increases and c decreases by a sufficient amount that the new cost structure is
adopted. Then production seasonality, as represented by peak-trough ratio * */B Aq q , decreases if
greater than unity and does not change if equal to unity.
This proposition would suggest that capital intensity induced productivity growth should
precede deseasonalization. It is not a contradiction of proposition 1 because causality between
series can be two-way, each re-enforcing the other. Note though that it is only when there is a
base of capital intensive innovations, i.e., 0F , that the model suggests productivity growth
should precede deseasonalization. When F is low, one should expect to see deseasonalization
before capital intensity induced productivity growth in order to establish a capital base in the
production system.
14
CLAIM 3. For low capital intensity farms, deseasonalization should precede capital intensity
induced productivity growth. For high capital intensity farms, capital intensity induced
productivity growth should precede deseasonalization.
Empirical Relationships between Productivity and Seasonality
We have just identified conditions under which an increase in productivity can induce a
reduction in seasonality and under which the reversed causal relationship can pertain. From this
perspective, Cov( , )E P
in table 7 warrants further scrutiny. We test for causal pathways in
Northern hemisphere milk production data.
Since the work of Yule, the danger of spurious regressions in testing for causality among
time series has been recognized. Evaluating the relationship of economic time-series data often
results in highly autocorrelated residuals and may bias conventional hypothesis tests (Granger
and Newbold). To circumvent this problem, it has become common practice to first test for
cointegration among the series. If series are known to be integrated of order one, denoted by
I(1), but not cointegrated, the practice is to estimate a vector autoregressive regression (VAR)
model on differences. Alternatively, if the series are known to be cointegrated then causality can
be determined using an error-correction model. Since the procedure will depend on the result of
the pretest, we adopt a procedure proposed by Dolado and Lütkepohl. This procedure is robust
to the degree of cointegration and so avoids possible problems with pretesting. Nonetheless, we
will first test for unit roots and cointegration.
Stationarity Tests
Using the Dickey-Fuller procedure we test for the stationarity in the E
and P indices. The
Dickey-Fuller test is restrictive in that it assumes statistically independent error terms of constant
variance. Phillips and Perron have developed a generalization of the Dickey-Fuller procedure
that relaxes the assumption on the error terms, but their test is problematic when the true model
15
contains a negative moving average. Because the true model is never known, Enders suggests
performing both tests. We do so and the results for P and E are reported in table 8, both at the
country and US state level. The table shows the test statistics, followed by the p-value in
parentheses and the number of lags used in brackets. We cannot reject a unit root in most cases.
For German milk, the null of a unit root in E
is rejected according to both augmented Dickey-
Fuller and Phillips-Perron tests. For US pork, it is rejected under the augmented Dickey-Fuller
test. For all states, evidence is inconclusive on the existence of a unit root in E . While it is
rejected according to the augmented Dickey-Fuller (Phillips-Perron) test in CA, IN, MI, NY,
OH, WA (ID, MN) it is then accepted in the other test. The existence of a unit root in the
productivity series is only rejected at the 10% level in KY under both tests, according to the
Phillips-Perron test in CA and TX, and according to the augmented Dickey-Fuller test in WA.
Cointegration
Assuming that unit roots do exist, we proceed with tests of cointegration. We use the Johansen
maximum-likelihood method (Johansen; Johansen and Juselius) that is based on a full system
approach. Cointegration is tested for based on the trace statistics of the integrating vectors. In
addition, the Engle-Granger method is used. The latter is a single equation method and it tests
for the unit root in the residual of these cointegrating regressions.
The results are reported in table 9. The results obtained using the Engle-Granger method
suggest that the productivity and seasonality series are cointegrated in PA and WA. The
outcome of the Johansen method provides even more evidence of the need to accommodate
possible cointegration. The trace test rejects the null hypothesis of no cointegration (rank of the
characteristic roots equal to zero) for milk in the UK, CA, OH , PA, and WA. As explained
below, the way in which causality tests are conducted depends on the presence of integrated
and/or cointegrated series.
16
Causality
Standard Granger-causality tests have nonstandard asymptotic properties if the variables of a
VAR are integrated or cointegrated. This complicates the tests for causality because one has to
recourse to simulations to determine the critical value in a causality test. The standard approach
in this case has been to estimate a VAR in differences if the variables are known to be I(1) but
not cointegrated, or to estimate an error-correction model if the variables are known to be
cointegrated (Mosconi and Giannini). An alternative is to employ an approach developed by
Dolado and Lütkepohl and been employed in, e.g., Tsionas. Dolado and Lütkepohl have shown
that if variables are dI and the true data-generating process is pVAR , then fitting
dpVAR results in the usual asymmptotics for Wald tests. This works because over-
parameterization of the VAR process avoids singularity in the test statistic. As Tsionas explains,
in order to test for causality fit a VAR( )p d in levels and then apply a standard F-test
involving the coefficients of lags 1 to p.
The VAR( )p d model for the commodity in state j is
(5)
, 1
,
, 1
, ,0 11 1 1 1 1 11 1 1 1 1
, , 10 21 2 2 1 2 21 2 2 1 2
,
, 1
,
j t
j t p
j t p
j j j j j j j jj t j t p dp p p d p p p d
j j j j j j j jj t j tp p p d p p p d
j t p
j t p
j t p d
a a a a a b b b b
b a a a a b b b b
E
E
E
E E
P P
P
P
P
17
where , , 1 ,( , , ... , )j t j t j t p dP P P is the vector of productivities for the commodity in region j at
time t. The ..ja
and ..
jb parameters pertain to the seasonality and productivity indicators,
respectively. The true VAR model is thought to go up to lag p, and the remaining d lags are
included to make estimates amenable to Wald tests (Dolado and Lütkepohl). According to
Dolado and Lütkepohl the following causality tests are performed. For deseasonalization to
cause productivity gains, 0 21 22 2: ... 0pH a a a should be rejected. For productivity gains
to precede deseasonalization, 0 11 12 1: ... 0pH b b b should be rejected.
As to the formal test of (5), it is based on the assumption that the structural relationship and
the parameters, such as mean, variance and trend, do not change over time. When dealing with
long time series this assumption is likely unrealistic and structural breaks in at least one
parameter are likely. A classical testing procedure for structural change is based on Chow’s test,
which applies for a known break date. The sample is split into two subsamples, estimates are
made of the parameters for each subsample and an F-test is applied on the equality of
parameters. The limit of this test is that the break-date must be known a priori (Hansen).
Alternatively the timing of the structural change can be estimated. As we have no a priori
knowledge of any break in the relationship, we would like the data to tell us if and when a break
occurred. Bai (1997) proposes a least squares estimation of a change point in multiple
regressions. The analysis is extended in Bai and Perron and Bai, Lumsdaine and Stock in two
ways. Bai and Perron develop the procedure to estimate multiple structural changes occurring at
unknown dates. Bai, Lumsdaine and Stock construct confidence intervals for the date of a single
break in multivariate time series, including I(0), I(1) and deterministically trending regressors.
In this latter test, the width of the asymptotic confidence interval does not decrease with sample
size, but is inversely related to the number of series that have a common break date. A similar
approach is developed in Murray and Papell. The approach of estimating a single break point on
18
multivariate time series proposed in Bai, Lumsdaine and Stock is extended to multiple break
points in Bai (2000).
Following Bai (2000) we use a quasi-likelihood ratio procedure to estimate the change date.
For the VAR( p+d) model in (5), the method compares the quasi-likelihood ratio estimated over
the entire sample based on a single parameter vector with the pair of quasi-likelihood ratios
obtained by estimating over the period before and the period after the break. If the whole sample
log quasi-likelihood exceeds the sum across the pair of time periods, then we assert that a break
is not present and we choose the whole sample estimates. Otherwise, we assert a break at the
identified point. Since in the case with a break the subsample estimates are completely
independent, all parameters including the variance of the error term may differ. With this
approach to estimating the VAR( p+d) model we apply the procedure of Dolado and Lütkepohl
to test for causality.
Results for sovereign countries and US states are presented in table 10. The first column
indicates the country/state and commodity. For each pair, but with three exceptions, tests are
performed on two periods. Two exceptions are TX-Milk and WA-Milk, for which no date break
was detected. The third exception is US-Milk where we detect a second break. The break year
is indicated in the third column, and is the year in which the earlier parameter regime ends. Note
that the beginning year of the first regime and the end year of the final regime depend on data
availability as indicated in table 2.6 The 4th column reports on the optimal number of lags, p, to
be included in the VAR analysis based on the Schwartz-Bayesian Information criterion.
The results of the causality tests are reported in columns 5-6 and 7-8. Columns 5 and 6
report the test statistic and respective p-value on the test that productivity growth causes, or
precedes, a decline in seasonality. Columns 7 and 8 do the same for the reverse hypothesis that a
6 We would have liked to base this analysis on time series of equal length, and this would require us to restrict the dates covered to the lowest common denominator. But the longest time series available in our sample reveals interesting results that differ from those exhibited by shorter time series, and we decided to use the maximum information available in our analysis.
19
decline in seasonality precedes productivity growth. Note that the hypotheses are not mutually
exclusive. It could happen that both hypotheses are accepted (two-way causality), or that neither
hypothesis is accepted (no causality). To help the reader in interpreting the results, we include a
final column indicating any detected causal relationship.
We turn first to the results on sovereign countries. For dairy, only milk production in the US
gives a significant result in the causality test. There are two breaks, 1957 and 1979.7 The test
shows that for the period prior to 1957, deseasonalization (growth in E ) preceded productivity
growth. For each other country and commodity, there is one break and it occurs early in the last
quarter of the Century. For instance with CAN-Milk, UK-Milk and US-Pork the break occurs in
the early 1980s while it occurs at about 1975 for milk in Germany.
Looking at dairy in US states in the lower part of table 10, there are significant results in the
causality test for CA, ID, and VA in the second time regime and these regimes start around about
1974. As for KY, the results indicate that productivity preceded E in the period up to 1979.
The result for New York is quite distinct. Here we observe causality going from E to P during
the first period, lasting up to 1976.
Although the picture could be clearer, a possible interpretation of the results goes as follows.
Consistent with proposition 1, during the 1930s-1950s technical progress was only made
possible after production seasonality became sufficiently low that return on capital exceeded the
cost of capital. This interpretation is suggested by the US-Milk result. Capital intensive
technology adoption then continued to the point where the high levels of installed capital
requires further endogenous changes in equilibrium production seasonality to be biased toward
aseasonality. For dairy in US states evidence suggests that, from about 1970 onward,
productivity growth fostered less seasonal agriculture. This is observed in California, Idaho, and
Virginia. For Kentucky, and arguably also for Canada, this trend is observed during the first
7 Using CUSUM and Chow test analysis, Erdogdu also found evidence of structural change in US livestock production seasonality.
20
period. But as break points are estimated independently, it happens that the break point is
relatively late in those two areas (1979 and 1983). Perhaps in these cases much of this causality
has been captured in the first period and not the second. At variance to the other states is New
York, where we observe causality from E to P in the first period. But again, this first period
ends in 1976, and it may pick up a belated trend from the first period that we detected at the US
level in dairying.8
Corroborating evidence for conclusions in table 10 is provided by figure 1 and data on the
capitalization of US farms during the period 1935-45. During that wartime period, capital
availability was extremely limited in the UK and the US; capital on US farms actually declined
(Gardner). And only in this period do we observe increases in seasonality in both the US and the
UK. In the 1980s capital declined as well on US farms during the farm crisis of that time, but
deseasonalization of dairy production continued unabated. This suggests that the possible link
between seasonality and capital depth has changed over these periods.
Discussion
Evidence presented provides qualified support for the hypothesis that deseasonalization was first
necessary to induce productivity growth and only then did productivity growth precede lower
seasonality. Placing our analysis in context with macroeconomic writing on industrialization, we
note that industrial agriculture has adapted widely from manufacturing innovations. These
adaptations have tended to be capital intensive, supporting the idea that spillovers from
industrialization in other sectors can lay the foundations for an industrialized format in animal
agriculture. A cause for delay may have been limited knowledge on and control of animal
8 Remember that US dairy data is available since 1930, but state-level data series commence in 1950. With the US milk regime break in 1957, most of the data that identified E P is not available at state-level. Indeed at the US level we find a second break in 1979, similar to the breaks identified across different US states.
21
biology, as reflected by the high level of production seasonality. Innovations surrounding
bioengineering since the early 1950s may have removed this impediment.
An alternative hypothesis we cannot rule out without further data analysis is simultaneity,
where both deseasonalization and productivity growth occur together.9 One important limitation
of our analysis is that the available time series are too short. To clearly identify the importance
of deseasonalization early in the industrialization of animal growing, time series have to start
before WW-II and this type of data was available to us only for US-Milk.
With the importance of aseasonality induced productivity growth commencing in the late
seventies or early eighties for most US states, it would be interesting to find out if it arose
directly through changes in production and processing technologies, or through less direct routes.
Agency and firm governance effects may have played a role. Sumner and Wolf use the 1993
Farm Cost and Returns Survey to discuss the impact of vertical integration on dairy production
structure.10 They show that the degree of vertical integration is much larger in the Pacific states
of the US, the states that have taken production share from the traditional dairy regions of the
Upper Midwest and Northeast in the past 30 years.
9 A theoretical foundation for the idea of simultaneity can be developed from equilibrium in systems with generalized complementarities. See Milgrom, Qian, and Roberts (1991) for a model identifying conditions supporting sequential directed adjustments in industry behavior that, as time intervals decline to zero, would support simultaneous adjustments. 10 The dairy states we analyzed do not coincide with those of the US Department of Agriculture Farm Cost and Returns Survey as analysed in Sumner and Wolf. There Georgia, Florida, Missouri, and Vermont are included, but Idaho, Illinois, Indiana, and Virginia are not.
22
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26
Table 1. Seasonal Bias in Noteworthy Dairy Production Innovations, 1900-2000
Pro-seasonal Seasonality neutral Anti-seasonal P1. Electric fencing P2. Irrigation technologies P3. Forage preservation
innovations P4. Storage innovations
for dairy output
N1. Genetic Innovation N2. Antibiotics N3. Sanitation technologies N4. Fertilization technologies N5. Tractor
A1. Artificial insemination A2. Housing innovations A3. Electricity in milking parlor A4. Refrigerated bulk tanks A5. Transfer pipes to bulk tanks A6. Mechanized feed handling A7. Robotic milking machines A8. Downstream processing A9. Bulk milk handling/marketing A10. Manure handling methods A11. Specialization in other outputs A12. National transportation and storage innovations for feed
Table 2. Monthly Production Data Used
Product Country Series Units Time covered Source
Milk US Milk Production Mill lbs 1930 - 2000 USDA-NASS DE Delivery to dairies Mill liters 1951 - 2001 Agrarwirtschaft CAN Milk Production 000 liters 1945 - 2000 Statistics Canada UK Milk Production Mill liters 1936 - 2002 Up to Nov-1994 UK Milk
Marketing Board, starting Dec 1994 Rural Payments Agency
Pork USa Production Mill lbs 1944 - 1981; 1983 - 2000
USDA-NASS
DEb Production 000 tons 1951 - 1989; 1991 - 2000
Agrarwirtschaft
UK Production 000 heads 1973 - 2000 DEFRA Beef USa Production Mill lbs 1944 - 1981;
1983 - 2000 USDA-NASS
DE Slaughter 000 heads 1951 - 2000 Agrarwirtschaft UK Slaughter 000 heads 1973 - 2000 DEFRA
a US pork and beef monthly production data are missing in 1982, a year the NASS service suffered severe budget cuts. To fill in the gap in the time series data, the calculated E was filled in using a cubic trend function. b No coherent monthly production data are available for DE pork in the unification year, 1990.
27
Table 3a. Indices of Seasonal Production, Averages per Decade
Peak-Trough Ratioa Entropy Indexb
1930-39 1950-59 1970-79 1990-99 1930-39 1950-59 1970-79 1990-99
Milk US 1.5190
1.4940
1.2361
1.1444
2.4746 2.4759
2.4828
2.4842 CAN
- 2.3164
1.6990
1.1208
- 2.4447
2.4699
2.4842 UK 1.4762
1.3996
1.3913
1.2060
2.4765 2.4791
2.4794
2.4833 DE - 1.6512
1.4519
1.2182
- 2.4708
2.4772
2.4829
Pork
US - 1.6294
1.3919
1.2668
- 2.4728
2.4804
2.4824 UK - - 1.3980
1.4198
- - 2.4788
2.4789 DE - 1.3007
1.1616
1.2194
- 2.4817
2.4839
2.4833
Beef
US - 1.2855
1.2207
1.2096
- 2.4823
2.4833
2.4832 UK - - 1.5736
1.8329
- - 2.4750
2.4708 DE - 1.4325
1.3455
1.4542
- 2.4784
2.4805
2.4785
a A decline in the index represents a decline in the seasonality of production. b A rise in the index represents a decline in the seasonality of production.
Table 3b. Indices of Seasonal Production, Averages per Decade
Peak-Trough Ratio Entropy Indexb
State 1950-59 1970-79 1990-99 1950-59 1970-79 1990-99
California 1.262 1.159 1.087 2.4818 2.4838 2.4846 Idaho 1.498 1.259 1.158 2.4754 2.4822 2.4836 Illinois 1.468 1.205 1.146 2.4773 2.4831 2.4837 Indiana 1.518 1.174 1.110 2.4755 2.4837 2.4843 Kentucky 1.742 1.445 1.184 2.4647 2.4779 2.4834 Michigan 1.435 1.107 1.084 2.4786 2.4844 2.4846 Minnesota 1.927 1.465 1.153 2.4613 2.4750 2.4835 New York 1.505 1.227 1.105 2.4751 2.4825 2.4844 Ohio 1.413 1.191 1.122 2.4782 2.4835 2.4841 Pennsylvania 1.367 1.157 1.101 2.4802 2.4839 2.4844 Texas 1.320 1.145 1.302 2.4804 2.4839 2.4808 Virginia 1.386 1.150 1.149 2.4778 2.4838 2.4840 Washington 1.498 1.184 1.083 2.4761 2.4835 2.4846 Wisconsin 1.695 1.322 1.134 2.4697 2.4809 2.4841
a A decline in the index represents a decline in the seasonality of production. b A rise in the index represents a decline in the seasonality of production.
28
Table 4. Dairy Production Shares by U.S. State and by Decade, 1950-2002
State 1950
1960
1970
1980
1990
2002
California 5.1
6.5 a 8.1
10.6
14.2
20.5
Idaho 1.0
1.3
1.3
1.5
2.0
4.8
Illinois 4.5
3.4
2.4
2.0
1.7
1.2
Indiana 3.2
2.6
2.0
1.7
1.5
1.5
Kentucky 2.1
2.1
2.1
1.7
1.5
1.0
Michigan 4.6
4.2
3.9
3.9
3.5
3.5
Minnesota 6.9
8.4
8.2
7.4
6.8
5.0
New York 7.6
8.4
8.8
8.5
7.5
7.2
Ohio 4.5
4.3
3.8
3.4
3.2
2.6
Pennsylvania 4.8
5.6
6.1
6.6
6.8
6.3
Texas 3.0
2.4
2.6
2.8
3.7
3.1
Virginia 1.7
1.5
1.5
1.5
1.4
1.1
Washington 1.5
1.5
1.8
2.3
3.0
3.3
Wisconsin 12.7
14.3
15.8
17.4
16.4
13.0
H , US level 407
501
566
651
691
786
a The arrows indicate the direction of change in shares since the previous decade.
29
Table 5. Trends in Deseasonalization–Animal Production in Selected Countries
0a , (t-value)a 1a , (t-value) 2R
Durbin-Watson p-value, 0 1(1 )a a E
Milk UK 0.391**
(0.170) 0.842*** (0.068)
0.703 2.304 0.021
DE 0.207* (0.122)
0.917*** (0.049)
0.879 2.841 0.089
CAN 0.062 (0.043)
0.975*** (0.030
0.939 2.631 0.151
US 0.076 (0.075)
0.969*** (0.030)
0.983 2.608 0.306
Pork UK 1.234**
(0.479) 0.502** (0.193)
0.212 2.044 0.010
DE 2.046*** (0.193)
0.176** (0.078)
0.098 1.708 0.000
US 0.809*** (0.250)
0.673*** (0.101)
0.456 2.222 0.001
Beef UK 1.599***
(0.457) 0.354*
(0.185) 0.128 1.996 0.000
DE 2.469*** (0.360)
0.004 (0.145)
0.001 1.965 0.000
US 2.198*** (0.339)
0.114 (0.137)
0.013 2.002 0.000
a *, **, and *** identify significance at the 10%, 5%, and 1% levels, respectively.
30
Table 6. Trends in Deseasonalization–Dairy Production in Selected US States
0a , (t-value)a 1a , (t-value) 2R
Durbin-Watson p-value, 0 1(1 )a a E
CA 0.470***
(0.119) 0.811*** (0.048)
0.848 3.039 0.000
ID 0.362*** (0.108)
0.854*** (0.043)
0.886 2.361 0.001
IL 0.351** (0.141)
0.859*** (0.057)
0.820 2.423 0.013
IN 0.229*** (0.084)
0.908*** (0.034)
0.934 2.379 0.007
KY 0.322 (0.116)
0.870*** (0.047)
0.874 2.749 0.005
MI 0.228*** (0.063)
0.908*** (0.026)
0.962 2.087 0.000
MN 0.176 (0.112)
0.929*** (0.045)
0.894 2.799 0.116
NY 0.247* (0.088)
0.900*** (0.035)
0.928 2.741 0.005
OH 0.458*** (0.135)
0.815*** (0.054)
0.818 2.700 0.001
PA 0.272** (0.131)
0.890*** (0.053)
0.851 2.843 0.037
TX 0.558*** (0.172)
0.775*** (0.069)
0.714 2.086 0.001
VA 0.302*** (0.098)
0.878*** (0.039)
0.908 2.819 0.002
WA 0.266*** (0.060)
0.893*** (0.024)
0.964 2.659 0.000
WI 0.267*** (0.098)
0.892*** (0.039)
0.911 2.378 0.006
a *, **, and *** identify significance at the 10%, 5%, and 1% levels, respectively.
31
Table 7. Correlation between Production Shares, Seasonality and Productivity in 14 Dairy States in 1950 and 2000
E
P
1950 2000 1950 2000
Shares -0.231 0.256 0.459 0.402 E
0.194 0.358
Table 8. Unit-Root Tests for Entropy and Productivity in Milk Production
E
P
Augmented Dickey-Fuller
Phillips-Perron Augmented Dickey-Fuller
Phillips-Perron
US-Milk - 2.847 (0.180) 10
- 9.722 (0.455) 10
- 1.484 (0.835) 2
- 2.281 (0962) 2
CAN-Milk 0.138 (0.995) 3
- 4.584 (0.850) 3
- 0.332 (0.989) [2] - 0.926 (0.989) [2] UK-Milk - 2.141 (0.523) [2] - 17.964 (0.106) [2] - 1.605 (0.790) [2] - 14.281 (0.212] [2] DE-Milk - 3.669 (0.024) 2
- 31.356 (0.007) 2
- 1.300 (0.888) 5
- 6.298 (0.722) 5
US-Pork -4.745 (0.001) [10] - 37.025 (0.002) [10] 0.049 (0.995) [2] - 1.909 (0.972) [2]
US States-milk California - 3.989 (0.009) 2
- 13.013 (0.266) 2
- 2.897 (0.163) 2
- 28.111 (0.013) 2
Idaho - 2.681 (0.244) 10
- 19.550 (0.077) 10
- 0.664 (0.975) 4
- 2.067 (0.968) 4
Illinois - 0.876 (0.959) 4
- 9.474 (0.473) 4
- 1.041 (0.938) 2
- 3.328 (0.922) 4
Indiana - 4.830 (0.0004) 6
- 3.061 (0.934) 6
- 1.862 (0.674) 3
- 7.301 (0.640) 3
Kentucky - 0.756 (0.969) 3
- 16.303 (0.145) 3
- 3.688 (0.023) 3
- 24.012 (0.031) 3
Michigan - 3.534 (0.036) 2
- 3.661 (0.906) 2
- 1.554 (0.810) 2
- 7.625 (0.614) 2
Minnesota - 1.002 (0.944) 4
- 24.935 (0.026) 4
- 1.298 (0.888) 2
- 5.144 (0.811) 2
New York - 4.190 (0.005) 9
- 6.943 (0.669) 9
- 1.435 (0.850) 2
- 5.915 (0.752) 2
Ohio - 5.153 (0.0001) 2
- 8.773 (0.524) 2
- 1.668 (0765) 9
- 16.116 (0.151) 9
Pennsylvania - 0.767 (0.968) 4
- 12.154 (0.308) 4
- 1.602 (0.791) 2
- 5.574 (0.779) 2
Texas - 0.894 (0.957) 10
- 8.917 (0.513) 10
- 1.994 (0.605) 3
- 20.738 (0.061) 3
Virginia - 1.429 (0.852) 10
- 5.396 (0.792) 10
- 1.634 (0.524) 2
- 8.774 (0.524) 2
Washington - 4.731 (0.001) 10
- 5.918 (0.752) 10
- 3.252 (0.075) 10
- 9.585 (0.465) 2
Wisconsin - 2.418 (0.370) 6
- 8.054 (0.579) 6
- 2.307 (0.430) 2
- 10.942 (0.376) 2
32
Table 9. Johansen and Engle-Granger test
Johansena Engel–Grangerb
(H0: no cointegration)
Trace Statistic Dep. Var. t-test p-value
US- E -Milk 12.839 (0.244) [2] US-Milk- E
US-Milk- P
-2.795 -0.493
0.361 [10] 0.994 [7]
CAN- E
12.705 (0.250) [1] CAN-Milk- E
CAN-Milk- P
-2.043 -2.111
0.753 [2] 0.723 [2]
UK- E
21.879 (0.015) [1] UK-Milk- E
UK-Milk- P
-3.079 -2.827
0.231 [4] 0.345 [10]
DE-Milk- E
- 3.042 0.246 4
DE- E
15.619 (0.114) [2] DE-Milk- P
- 0.738 0.989 2
US- E -Pork 13.258 (0.218) [11] US-Pork- E
US-Pork- P
-1.560 -1.674
0.909 [10] 0.882 [7]
US-States (milk only) CA- E
- 2.935 0.293 2
CA- E
35.148 (0.0004) 1
CA- P
- 3.060 0.238 2
ID- E
- 2.946 0.288 2
ID- E
12.269 (0.284) 2
ID- P
- 2.084 0.735 2
IL- E
- 3.227 0.176 2
IL- E
15.079 (0.133) 1
IL- P
- 1.879 0.818 2
IN- E
- 2.257 0.652 3
IN- E
11.151 (0.372) 2
IN- P
- 2.072 0.741 3
KY- E
- 1.110 0.970 3
KY- E
14.030 (0.177) 6
KY- P
- 3.450 0.111 3
MI- E
- 2.347 0.604 2
MI- E
15.494 (0.118) 2
MI- P
- 2.193 0.683 2
MN- E
- 2.493 0.524 4
MN- E
8.450 (0.608) 3
MN- P
- 2.270 0.645 2
NY- E
- 1.798 0.846 2
NY- E
14.433 (0.159) 1
NY- P
- 1.863 0.824 2
OH- E
- 1.743 0.863 3
OH- E
22.494 (0.013) 9
OH- P
- 1.745 0.862 9
PA- E
- 3.536 0.091 2
PA- E
21.920 (0.015) 3
PA- P
- 3.628 0.074 2
TX- E
- 1.139 0.968 10
TX- E
9.684 (0.500) 11
TX- P
- 2.559 0.487 2
VA- E
- 1.423 0.960 10
VA- E
13.066 (0.230) 2
VA- P
- 1.986 0.777 2
WA- E
- 2.325 0.616 2
WA- E
24.755 (0.007) 3
WA- P
- 3.496 0.100 2
WI- E
- 2.866 0.325 2
WI- E
23.208 (0.011) 1
WI- P
- 3.094 0.225 2
33
a Trace statistic stands for the Johansen trace statistic using a finite-sample correction (Hall and Cummins). The null hypothesis of p=0 indicates tests for no cointegration against the alternative of one or more cointgrating vectors (p>0). The p-value is reported in parentheses. The optimal lag length has been chosen using the Akaike-Information Criterion and is indicated in brackets. b In the Engle-Granger method a large p-value shows evidence against cointegration. The optimal lag length has been chosen using the Akaike-Information Criterion and is indicated in brackets.
34
Table 10. Dolado and Lütkepohl Causality Test for Aseasonality and Productivitya
State/ Commodity
Causality Break Year
Number of lags pb
P E
E P
Conclusion
2 -test p-value 2 -test p-value
Countries 1st period 0.228 0.633 2.789
0.095 E P
2nd period 0.401 0.527 0.064
0.801 - US-Milk 3rd period
1957, 1979
1 0.181 0.670 0.149
0.699 -
1st period 1983 1.918 0.166 0.001
0.975 - CAN-Milk
2nd period 1
0.008 0.927 0.002
0.966 -
1st period 1984 0.008 0.806 0.187
0.666 - UK-Milk
2nd period 1
0.073 0.787 0.139
0.710 - 1st period 1975 0.018 0.893 0.159
0.690 - DE-Milk
2nd period 2
0.010 0.920 1.014
0.314 -
1st period 1981 0.009 0.308 0.042
0.837 - US-Pork
2nd period 2
0.215 0.643 0.005
0.823 -
US-States Milk 1st period 0.023 0.881 0.643
0.423 - CA 2nd period 1972 2 4.871 0.027 0.192
0.661 P E
1st period 0.002 0.734 0.906
0.341 - ID 2nd period 1976 1 14.494 0.000 0.020
0.887 P E
1st period 2.086 0.149 0.791
0.374 - IL
2nd period 1977 1
0.041 0.840 0.082
0.775 -
1st period 0.340 0.560 1.410
0.235 - IN
2nd period 1984 1
0.379 0.538 0.055
0.814 -
1st period 3.994 0.046 1.713
0.191 P E
KY 2nd period
1979 1 0.030 0.862 0.002
0.969 -
1st period 0.030 0.863 0.345
0.557 - MI
2nd period 1967 1
1.003 0.316 0.137
0.712 -
1st period 0.209 0.648 0.069
0.793 - MN
2nd period 1982 2
0.114 0.735 1.301
0.254 -
1st period 0.059 0.808 3.219
0.073 E P
NY 2nd period
1976 1 0.000 0.881 2.378
0.985 -
1st period 0.111 0.739 0.319
0.572 - OH
2nd period 1971 2
0.639 0.424 1.314
0.252 -
1st period 0.378 0.539 1.074
0.300 - PA
2nd period 1967 1
0.403 0.526 0.865
0.352 -
TX None 2 0.054 0.817 1.373 0.241 -
1st period 0.001 0.817 0.002
0.961 - VA 2nd period 1972 1 14.409 0.000 0.271
0.603 P E
WA None 3 0.068 0.794 0.028 0.867 -
1st period 0.129 0.719 1.315
0.252 - WI
2nd period 1974 1
0.159 0.207 1.237
0.266 -
35
a In this test, proceed by fitting a ( )VAR p d in levels and apply a standard F-test involving the coefficients of lags 1 to p. The H0 states that the parameters of lag 1 to p to the causal variable are zero. b The optimal number of lags was chosen according to the Schwartz-Bayesian Information Criterion.
Peak-Trough-Ratio Dairy Production
0.0
0.5
1.0
1.5
2.0
2.5
3.0
US CAN UK DE
1930-39
1940-49
1950-59
1960-69
1970-79
1980-89
1990-2000
Figure 1. Changing Peak-Trough Ratios of Dairy Production in Selected Countries.
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